{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Negative Binomial Regression (Students absence example)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Negative binomial distribution review"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The negative binomial distribution is flexible with multiple possible formulations. For example, it can model the number of *trials* or *failures* in a sequence of independent Bernoulli trials with probability of success (or failure) $p$ until the $k$-th \"success\". If we want to model the number of trials until the $k$-th success, the probability mass function (pmf) results:\n",
    "\n",
    "$$\n",
    "p(y | k, p)= \\binom{y - 1}{y-k}(1 -p)^{y - k}p^k\n",
    "$$\n",
    "\n",
    "where $0 \\le p \\le 1$ is the probability of success in each Bernoulli trial, $k > 0$, usually integer, $y \\in \\{k, k + 1, \\cdots\\}$ and $Y$ is the number of trials until the $k$-th success.\n",
    "\n",
    "In this case, since we are modeling the number of *trials* until the $k$-th success, $y$ starts at $k$ and can be any integer greater than or equal to $k$. If instead we want to model the number of *failures* until the $k$-th success, we can use the same definition but $Y$ represents failures and starts at $0$ and there's a slightly different pmf:\n",
    "\n",
    "$$\n",
    "p(y | k, p)= \\binom{y + k - 1}{k-1}(1 -p)^{y}p^k\n",
    "$$\n",
    "\n",
    "In this case, $y$ starts at $0$ and can be any integer greater than or equal to $0$. When modeling failures, $y$ starts at 0, when modeling trials, $y$ starts at $k$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "These are not the only ways of defining the negative binomial distribution, there are plenty of options! One of the most interesting, and the one you see in [PyMC](https://www.pymc.io/projects/docs/en/stable/api/distributions/generated/pymc.NegativeBinomial.html), the library we use in Bambi for the backend, is as a continuous mixture. The negative binomial distribution describes a Poisson random variable whose rate is also a random variable (not a fixed constant!) following a gamma distribution. Or in other words, conditional on a gamma-distributed variable $\\mu$, the variable $Y$ has a Poisson distribution with mean $\\mu$.\n",
    "\n",
    "Under this alternative definition, the pmf is\n",
    "\n",
    "$$\n",
    "\\displaystyle p(y | k, \\alpha) = \\binom{y + \\alpha - 1}{y} \\left(\\frac{\\alpha}{\\mu + \\alpha}\\right)^\\alpha\\left(\\frac{\\mu}{\\mu + \\alpha}\\right)^y\n",
    "$$\n",
    "\n",
    "where $\\mu$ is the parameter of the Poisson distribution (the mean, and variance too!) and $\\alpha$ is the rate parameter of the gamma."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings\n",
    "\n",
    "import arviz as az\n",
    "import bambi as bmb\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "from scipy.stats import nbinom\n",
    "\n",
    "az.style.use(\"arviz-darkgrid\")\n",
    "\n",
    "warnings.simplefilter(action='ignore', category=FutureWarning)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "SciPy uses the number of *failures* until $k$ successes definition, therefore $y$ starts at 0. In the following plot, we have  the probability of observing $y$ failures before we see $k=3$ successes. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = np.arange(0, 30)\n",
    "k = 3\n",
    "p1 = 0.5\n",
    "p2 = 0.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<Figure size 1200x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(12, 4), sharey=True)\n",
    "\n",
    "ax[0].bar(y, nbinom.pmf(y, k, p1))\n",
    "ax[0].set_xticks(np.linspace(0, 30, num=11))\n",
    "ax[0].set_title(f\"k = {k}, p = {p1}\")\n",
    "\n",
    "ax[1].bar(y, nbinom.pmf(y, k, p2))\n",
    "ax[1].set_xticks(np.linspace(0, 30, num=11))\n",
    "ax[1].set_title(f\"k = {k}, p = {p2}\")\n",
    "\n",
    "fig.suptitle(\"Y = Number of failures until k successes\", fontsize=16);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For example, when $p=0.5$, the probability of seeing $y=0$ failures before 3 successes (or in other words, the probability of having 3 successes out of 3 trials) is 0.125, and the probability of seeing $y=3$ failures before 3 successes is 0.156."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.12499999999999997\n",
      "0.15624999999999992\n"
     ]
    }
   ],
   "source": [
    "print(nbinom.pmf(y, k, p1)[0])\n",
    "print(nbinom.pmf(y, k, p1)[3])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To change the definition to the number of *trials* until $k$ successes, we just need to shift the whole thing to the right by adding $k$ to the $y$ values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1200x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 2, figsize=(12, 4), sharey=True)\n",
    "\n",
    "ax[0].bar(y + k, nbinom.pmf(y, k, p1))\n",
    "ax[0].set_xticks(np.linspace(3, 30, num=10))\n",
    "ax[0].set_title(f\"k = {k}, p = {p1}\")\n",
    "\n",
    "ax[1].bar(y + k, nbinom.pmf(y, k, p2))\n",
    "ax[1].set_xticks(np.linspace(3, 30, num=10))\n",
    "ax[1].set_title(f\"k = {k}, p = {p2}\")\n",
    "\n",
    "fig.suptitle(\"Y = Number of trials until k successes\", fontsize=16);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Negative binomial in GLM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The negative binomial distribution belongs to the exponential family, and the canonical link function is \n",
    "\n",
    "$$\n",
    "g(\\mu_i) = \\log\\left(\\frac{\\mu_i}{k + \\mu_i}\\right) = \\log\\left(\\frac{k}{\\mu_i} + 1\\right)\n",
    "$$\n",
    "\n",
    "but it is difficult to interpret. The log link is usually preferred because of the analogy with Poisson model, and it also tends to give better results."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load and explore Students data\n",
    "\n",
    "This example is based on this [UCLA example](https://stats.idre.ucla.edu/r/dae/negative-binomial-regression/).\n",
    "\n",
    "School administrators study the attendance behavior of high school juniors at two schools.  Predictors of the **number of days of absence** include the **type of program** in which the student is enrolled and a **standardized test in math**. We have attendance data on 314 high school juniors.\n",
    "\n",
    "The variables of interest in the dataset are\n",
    "\n",
    "* daysabs: The number of days of absence. It is our response variable.\n",
    "* progr: The type of program. Can be one of 'General', 'Academic', or 'Vocational'.\n",
    "* math: Score in a standardized math test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.read_stata(\"https://stats.idre.ucla.edu/stat/stata/dae/nb_data.dta\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>gender</th>\n",
       "      <th>math</th>\n",
       "      <th>daysabs</th>\n",
       "      <th>prog</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1001.0</td>\n",
       "      <td>male</td>\n",
       "      <td>63.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1002.0</td>\n",
       "      <td>male</td>\n",
       "      <td>27.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1003.0</td>\n",
       "      <td>female</td>\n",
       "      <td>20.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1004.0</td>\n",
       "      <td>female</td>\n",
       "      <td>16.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1005.0</td>\n",
       "      <td>female</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       id  gender  math  daysabs  prog\n",
       "0  1001.0    male  63.0      4.0   2.0\n",
       "1  1002.0    male  27.0      4.0   2.0\n",
       "2  1003.0  female  20.0      2.0   2.0\n",
       "3  1004.0  female  16.0      3.0   2.0\n",
       "4  1005.0  female   2.0      3.0   2.0"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We assign categories to the values 1, 2, and 3 of our `\"prog\"` variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>id</th>\n",
       "      <th>gender</th>\n",
       "      <th>math</th>\n",
       "      <th>daysabs</th>\n",
       "      <th>prog</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1001.0</td>\n",
       "      <td>male</td>\n",
       "      <td>63.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>Academic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1002.0</td>\n",
       "      <td>male</td>\n",
       "      <td>27.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>Academic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1003.0</td>\n",
       "      <td>female</td>\n",
       "      <td>20.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>Academic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1004.0</td>\n",
       "      <td>female</td>\n",
       "      <td>16.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>Academic</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1005.0</td>\n",
       "      <td>female</td>\n",
       "      <td>2.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>Academic</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       id  gender  math  daysabs      prog\n",
       "0  1001.0    male  63.0      4.0  Academic\n",
       "1  1002.0    male  27.0      4.0  Academic\n",
       "2  1003.0  female  20.0      2.0  Academic\n",
       "3  1004.0  female  16.0      3.0  Academic\n",
       "4  1005.0  female   2.0      3.0  Academic"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[\"prog\"] = data[\"prog\"].map({1: \"General\", 2: \"Academic\", 3: \"Vocational\"})\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Academic program is the most popular program (167/314) and General is the least popular one (40/314)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "prog\n",
       "Academic      167\n",
       "Vocational    107\n",
       "General        40\n",
       "Name: count, dtype: int64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data[\"prog\"].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's explore the distributions of math score and days of absence for each of the three programs listed above. The vertical lines indicate the mean values."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(3, 2, figsize=(8, 6), sharex=\"col\")\n",
    "programs = list(data[\"prog\"].unique())\n",
    "programs.sort()\n",
    "\n",
    "for idx, program in enumerate(programs):\n",
    "    # Histogram\n",
    "    ax[idx, 0].hist(data[data[\"prog\"] == program][\"math\"], edgecolor='black', alpha=0.9)\n",
    "    ax[idx, 0].axvline(data[data[\"prog\"] == program][\"math\"].mean(), color=\"C1\")\n",
    "\n",
    "    # Barplot\n",
    "    days = data[data[\"prog\"] == program][\"daysabs\"]\n",
    "    days_mean = days.mean()\n",
    "    days_counts = days.value_counts()\n",
    "    values = list(days_counts.index)\n",
    "    count = days_counts.values\n",
    "    ax[idx, 1].bar(values, count, edgecolor='black', alpha=0.9)\n",
    "    ax[idx, 1].axvline(days_mean, color=\"C1\")\n",
    "\n",
    "    # Titles\n",
    "    ax[idx, 0].set_title(program)\n",
    "    ax[idx, 1].set_title(program)\n",
    "\n",
    "plt.setp(ax[-1, 0], xlabel=\"Math score\")\n",
    "plt.setp(ax[-1, 1], xlabel=\"Days of absence\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first impression we have is that the distribution of math scores is not equal for any of the programs. It looks right-skewed for students under the Academic program, left-skewed for students under the Vocational program, and roughly uniform for students in the General program (although there's a drop in the highest values). Clearly those in the Vocational program has the highest mean for the math score.\n",
    " \n",
    "On the other hand, the distribution of the days of absence is right-skewed in all cases. Students in the General program present the highest absence mean while the Vocational group is the one who misses fewer classes on average."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Models\n",
    "\n",
    "We are interested in measuring the association between the type of the program and the math score with the days of absence. It's also of interest to see if the association between math score and days of absence is different in each type of program. \n",
    "\n",
    "In order to answer our questions, we are going to fit and compare two models. The first model uses the type of the program and the math score as predictors. The second model also includes the interaction between these two variables. The score in the math test is going to be standardized in both cases to make things easier for the sampler and save some seconds. A good idea to follow along is to run these models without scaling `math` and comparing how long it took to fit.\n",
    "\n",
    "We are going to use a negative binomial likelihood to model the days of absence. But let's stop here and think why we use this likelihood. Earlier, we said that the negative binomial distributon arises when our variable represents the number of trials until we got $k$ successes. However, the number of trials is fixed, i.e. the number of school days in a given year is not a random variable. So if we stick to the definition, we could think of the two alternative views for this problem\n",
    "\n",
    "* Each of the $n$ days is a trial, and we record whether the student is absent ($y=1$) or not ($y=0$). This corresponds to a binary regression setting, where we could think of logistic regression or something alike. A problem here is that we have the sum of $y$ for a student, but not the $n$.\n",
    "* The whole school year represents the space where events occur and we count how many absences we see in that space for each student. This gives us a Poisson regression setting (count of an event in a given space or time).\n",
    "\n",
    "We also know that when $n$ is large and $p$ is small, the Binomial distribution can be approximated with a Poisson distribution with $\\lambda = n * p$. We don't know exactly $n$ in this scenario, but we know it is around 180, and we do know that $p$ is small because you can't skip classes all the time. So both modeling approaches should give similar results.\n",
    "\n",
    "But then, why negative binomial? Can't we just use a Poisson likelihood?\n",
    "\n",
    "Yes, we can. However, using a Poisson likelihood implies that the mean is equal to the variance, and that is usually an unrealistic assumption. If it turns out the variance is either substantially smaller or greater than the mean, the Poisson regression model results in a poor fit. Alternatively, if we use a negative binomial likelihood, the variance is not forced to be equal to the mean, and there's more flexibility to handle a given dataset, and consequently, the fit tends to be better."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model 1 \n",
    "\n",
    "$$\n",
    "\\log(\\mathbb{E}[Y_i]) = \\beta_1 \\text{Academic}_i + \\beta_2 \\text{General}_i + \\beta_3 \\text{Vocational}_i + \\beta_4 \\text{Math\\_std}_i\n",
    "$$\n",
    "\n",
    "### Model 2\n",
    "\n",
    "$$\n",
    "\\begin{aligned}\n",
    "\\log(\\mathbb{E}[Y_i]) &= \\beta_1 \\text{Academic}_i + \\beta_2 \\text{General}_i + \\beta_3 \\text{Vocational}_i + \\beta_4 \\text{Math\\_std}_i + \\\\\n",
    "            & \\beta_5 \\text{General}_i \\cdot \\text{Math\\_std}_i + \\beta_6 \\text{Vocational}_i \\cdot \\text{Math\\_std}_i\n",
    "\\end{aligned}\n",
    "$$\n",
    "\n",
    "In both cases we have the following dummy variables\n",
    "\n",
    "\n",
    "$$\\text{Academic}_i = \n",
    "\\left\\{ \n",
    "    \\begin{array}{ll}\n",
    "        1 & \\textrm{if student is under Academic program} \\\\\n",
    "        0 & \\textrm{other case} \n",
    "    \\end{array}\n",
    "\\right.\n",
    "$$\n",
    "\n",
    "$$\\text{General}_i = \n",
    "\\left\\{ \n",
    "    \\begin{array}{ll}\n",
    "        1 & \\textrm{if student is under General program} \\\\\n",
    "        0 & \\textrm{other case} \n",
    "    \\end{array}\n",
    "\\right.\n",
    "$$\n",
    "\n",
    "$$\\text{Vocational}_i = \n",
    "\\left\\{ \n",
    "    \\begin{array}{ll}\n",
    "        1 & \\textrm{if student is under Vocational program} \\\\\n",
    "        0 & \\textrm{other case} \n",
    "    \\end{array}\n",
    "\\right.\n",
    "$$\n",
    "\n",
    "and $Y$ represents the days of absence.\n",
    "\n",
    "So, for example, the first model for a student under the Vocational program reduces to\n",
    "$$\n",
    "\\log(\\mathbb{E}[Y_i]) = \\beta_3 + \\beta_4 \\text{Math\\_std}_i\n",
    "$$\n",
    "\n",
    "And one last thing to note is we've decided not to include an intercept term, that's why you don't see any $\\beta_0$ above. This choice allows us to represent the effect of each program directly with $\\beta_1$, $\\beta_2$, and $\\beta_3$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model fit\n",
    "\n",
    "It's very easy to fit these models with Bambi. We just pass a formula describing the terms in the model and Bambi will know how to handle each of them correctly. The `0` on the right hand side of `~` simply means we don't want to have the intercept term that is added by default. `scale(math)` tells Bambi we want to use standardize `math` before being included in the model. By default, Bambi uses a log link for negative binomial GLMs. We'll stick to this default here.\n",
    "\n",
    "### Model 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [alpha, prog, scale(math)]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "14a19250f0cf4943b207127a87069c64",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 2 seconds.\n"
     ]
    }
   ],
   "source": [
    "model_additive = bmb.Model(\"daysabs ~ 0 + prog + scale(math)\", data, family=\"negativebinomial\")\n",
    "idata_additive = model_additive.fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model 2\n",
    "\n",
    "For this second model we just add `prog:scale(math)` to indicate the interaction. A shorthand would be to use `y ~ 0 + prog*scale(math)`, which uses the **full interaction** operator. In other words, it just means we want to include the interaction between `prog` and `scale(math)` as well as their main effects."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (4 chains in 4 jobs)\n",
      "NUTS: [alpha, prog, scale(math), prog:scale(math)]\n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "693b25ac989b451eaf397df090233d29",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"white-space:pre;overflow-x:auto;line-height:normal;font-family:Menlo,'DejaVu Sans Mono',consolas,'Courier New',monospace\"></pre>\n"
      ],
      "text/plain": []
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Sampling 4 chains for 1_000 tune and 1_000 draw iterations (4_000 + 4_000 draws total) took 2 seconds.\n"
     ]
    }
   ],
   "source": [
    "model_interaction = bmb.Model(\"daysabs ~ 0 + prog + scale(math) + prog:scale(math)\", data, family=\"negativebinomial\")\n",
    "idata_interaction = model_interaction.fit()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Explore models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The first thing we do is calling `az.summary()`. Here we pass the `InferenceData` object the `.fit()` returned. This prints information about the marginal posteriors for each parameter in the model as well as convergence diagnostics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <td>1.020</td>\n",
       "      <td>0.103</td>\n",
       "      <td>0.814</td>\n",
       "      <td>1.201</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.002</td>\n",
       "      <td>5417.0</td>\n",
       "      <td>3485.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>prog[Academic]</th>\n",
       "      <td>1.889</td>\n",
       "      <td>0.084</td>\n",
       "      <td>1.736</td>\n",
       "      <td>2.049</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>4463.0</td>\n",
       "      <td>2867.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>prog[General]</th>\n",
       "      <td>2.337</td>\n",
       "      <td>0.163</td>\n",
       "      <td>2.021</td>\n",
       "      <td>2.624</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>5724.0</td>\n",
       "      <td>3532.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>prog[Vocational]</th>\n",
       "      <td>1.048</td>\n",
       "      <td>0.115</td>\n",
       "      <td>0.833</td>\n",
       "      <td>1.267</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>4753.0</td>\n",
       "      <td>3242.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>scale(math)</th>\n",
       "      <td>-0.150</td>\n",
       "      <td>0.064</td>\n",
       "      <td>-0.272</td>\n",
       "      <td>-0.032</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>4660.0</td>\n",
       "      <td>3525.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                   mean     sd  hdi_3%  hdi_97%  mcse_mean  mcse_sd  ess_bulk  \\\n",
       "alpha             1.020  0.103   0.814    1.201      0.001    0.002    5417.0   \n",
       "prog[Academic]    1.889  0.084   1.736    2.049      0.001    0.001    4463.0   \n",
       "prog[General]     2.337  0.163   2.021    2.624      0.002    0.002    5724.0   \n",
       "prog[Vocational]  1.048  0.115   0.833    1.267      0.002    0.002    4753.0   \n",
       "scale(math)      -0.150  0.064  -0.272   -0.032      0.001    0.001    4660.0   \n",
       "\n",
       "                  ess_tail  r_hat  \n",
       "alpha               3485.0    1.0  \n",
       "prog[Academic]      2867.0    1.0  \n",
       "prog[General]       3532.0    1.0  \n",
       "prog[Vocational]    3242.0    1.0  \n",
       "scale(math)         3525.0    1.0  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_additive)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hdi_3%</th>\n",
       "      <th>hdi_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>alpha</th>\n",
       "      <td>1.017</td>\n",
       "      <td>0.104</td>\n",
       "      <td>0.835</td>\n",
       "      <td>1.226</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>4447.0</td>\n",
       "      <td>3111.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>prog[Academic]</th>\n",
       "      <td>1.878</td>\n",
       "      <td>0.084</td>\n",
       "      <td>1.726</td>\n",
       "      <td>2.042</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>4299.0</td>\n",
       "      <td>3428.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>prog[General]</th>\n",
       "      <td>2.346</td>\n",
       "      <td>0.172</td>\n",
       "      <td>2.023</td>\n",
       "      <td>2.666</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.003</td>\n",
       "      <td>4187.0</td>\n",
       "      <td>3052.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>prog[Vocational]</th>\n",
       "      <td>0.989</td>\n",
       "      <td>0.126</td>\n",
       "      <td>0.766</td>\n",
       "      <td>1.244</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>4067.0</td>\n",
       "      <td>3124.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>scale(math)</th>\n",
       "      <td>-0.194</td>\n",
       "      <td>0.080</td>\n",
       "      <td>-0.338</td>\n",
       "      <td>-0.036</td>\n",
       "      <td>0.001</td>\n",
       "      <td>0.001</td>\n",
       "      <td>3415.0</td>\n",
       "      <td>3184.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>prog:scale(math)[General]</th>\n",
       "      <td>0.014</td>\n",
       "      <td>0.168</td>\n",
       "      <td>-0.299</td>\n",
       "      <td>0.334</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>4051.0</td>\n",
       "      <td>3345.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>prog:scale(math)[Vocational]</th>\n",
       "      <td>0.196</td>\n",
       "      <td>0.164</td>\n",
       "      <td>-0.117</td>\n",
       "      <td>0.494</td>\n",
       "      <td>0.003</td>\n",
       "      <td>0.002</td>\n",
       "      <td>3669.0</td>\n",
       "      <td>2844.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                               mean     sd  hdi_3%  hdi_97%  mcse_mean  \\\n",
       "alpha                         1.017  0.104   0.835    1.226      0.002   \n",
       "prog[Academic]                1.878  0.084   1.726    2.042      0.001   \n",
       "prog[General]                 2.346  0.172   2.023    2.666      0.003   \n",
       "prog[Vocational]              0.989  0.126   0.766    1.244      0.002   \n",
       "scale(math)                  -0.194  0.080  -0.338   -0.036      0.001   \n",
       "prog:scale(math)[General]     0.014  0.168  -0.299    0.334      0.003   \n",
       "prog:scale(math)[Vocational]  0.196  0.164  -0.117    0.494      0.003   \n",
       "\n",
       "                              mcse_sd  ess_bulk  ess_tail  r_hat  \n",
       "alpha                           0.002    4447.0    3111.0    1.0  \n",
       "prog[Academic]                  0.001    4299.0    3428.0    1.0  \n",
       "prog[General]                   0.003    4187.0    3052.0    1.0  \n",
       "prog[Vocational]                0.002    4067.0    3124.0    1.0  \n",
       "scale(math)                     0.001    3415.0    3184.0    1.0  \n",
       "prog:scale(math)[General]       0.002    4051.0    3345.0    1.0  \n",
       "prog:scale(math)[Vocational]    0.002    3669.0    2844.0    1.0  "
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "az.summary(idata_interaction)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The information in the two tables above can be visualized in a more concise manner using a forest plot. ArviZ provides us with `plot_forest()`. There we simply pass a list containing the `InferenceData` objects of the models we want to compare."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_forest(\n",
    "    [idata_additive, idata_interaction],\n",
    "    model_names=[\"Additive\", \"Interaction\"],\n",
    "    var_names=[\"prog\", \"scale(math)\"],\n",
    "    combined=True,\n",
    "    figsize=(8, 4)\n",
    ");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One of the first things one can note when seeing this plot is the similarity between the marginal posteriors. Maybe one can conclude that the variability of the marginal posterior of `scale(math)` is slightly lower in the model that considers the interaction, but the difference is not significant. \n",
    "\n",
    "We can also make conclusions about the association between the program and the math score with the days of absence. First, we see the posterior for the Vocational group is to the left of the posterior for the two other programs, meaning it is associated with fewer absences (as we have seen when first exploring our data). There also seems to be a difference between General and Academic, where we may conclude the students in the General group tend to miss more classes.\n",
    "\n",
    "In addition, the marginal posterior for `math` shows negative values in both cases. This means that students with higher math scores tend to miss fewer classes. Below, we see a forest plot with the posteriors for the coefficients of the interaction effects. Both of them overlap with 0, which means the data does not give much evidence to support there is an interaction effect between program and math score (i.e., the association between math and days of absence is similar for all the programs)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "az.plot_forest(idata_interaction, var_names=[\"prog:scale(math)\"], combined=True, figsize=(8, 4))\n",
    "plt.axvline(0);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot predicted mean response\n",
    "\n",
    "We finish this example showing how we can get predictions for new data and plot the mean response for each program together with credible intervals."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Default computed for conditional variable: math, prog\n",
      "Default computed for conditional variable: math, prog\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(1, 2, figsize=(10, 5), sharey=True)\n",
    "\n",
    "bmb.interpret.plot_predictions(\n",
    "    model_additive,\n",
    "    idata_additive,\n",
    "    legend=False,\n",
    "    conditional=[\"math\", \"prog\"],\n",
    "    subplot_kwargs={\"main\": \"math\", \"group\": \"prog\"},\n",
    "    ax=axes[0]\n",
    ")\n",
    "\n",
    "bmb.interpret.plot_predictions(\n",
    "    model_interaction,\n",
    "    idata_interaction,\n",
    "    conditional=[\"math\", \"prog\"],\n",
    "    subplot_kwargs={\"main\": \"math\", \"group\": \"prog\"},\n",
    "    ax=axes[1],\n",
    ");\n",
    "\n",
    "axes[0].set(xlabel=\"Math score\", ylabel=\"Days abs\", title=\"Additive\", ylim=[0, 25])\n",
    "axes[1].set(xlabel=\"Math score\", ylabel=None, title=\"Interaction\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see in this plot, the interval for the mean response for the Vocational program does not overlap with the interval for the other two groups, representing the group of students who miss fewer classes. On the right panel we can also see that including interaction terms does not change the slopes significantly because the posterior distributions of these coefficients have a substantial overlap with 0."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you've made it to the end of this notebook and you're still curious about what else you can do with these two models, you're invited to use `az.compare()` to compare the fit of the two models. What do you expect before seeing the plot? Why? Is there anything else you could do to improve the fit of the model?\n",
    "\n",
    "Also, if you're still curious about what this model would have looked like with the Poisson likelihood, you just need to replace `family=\"negativebinomial\"` with `family=\"poisson\"` and then you're ready to compare results!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Last updated: Sun Sep 28 2025\n",
      "\n",
      "Python implementation: CPython\n",
      "Python version       : 3.13.7\n",
      "IPython version      : 9.4.0\n",
      "\n",
      "bambi     : 0.14.1.dev57+g7b2bb342c.d20250928\n",
      "pandas    : 2.3.2\n",
      "numpy     : 2.3.3\n",
      "matplotlib: 3.10.6\n",
      "arviz     : 0.22.0\n",
      "\n",
      "Watermark: 2.5.0\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%load_ext watermark\n",
    "%watermark -n -u -v -iv -w"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [conda env:base] *",
   "language": "python",
   "name": "conda-base-py"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
